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I'm reading studying a book: Principles of Quantum Computation and Information Volume I: Basic Concepts by Giuliano Benenti ... And I have a question on page 216 about Dense coding. In summary, we have:

  1. A source S generates an EPR pair shared by Alice and Bob. The EPR pair is prepared, for instance, in the state $|Φ^+⟩ = \frac{1}{\sqrt2}(|00⟩ + |11⟩)$ (OK)

  2. There are four possible values of the two classical bits that Alice wishes to send to Bob: 00, 01, 10 and 11. They determine the unitary operation U that Alice performs on her half of the EPR pair: $U = \{I, σ_x, σ_z, iσ_y\}$. (OK)

  3. Alice sends her half of the EPR pair to Bob. (??)

The entangled pair was not shared between Alice and Bob. Does one qubit stay with Alice and the other with Bob? So what does the author mean by sending the qubit to Bob? How is this done? That detail stopped me.

My context is quantum computing. What comes to mind in entanglement are two fixed and separate qubits, like two spins-1/2. Can someone help me understand please? Thanks.

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So to clarify, in your steps above, Alice and Bob each of one qubit of the entangled EPR pair in (1), Alice performs some gate on her qubit/half of the pair in (2) based on the two bits she wishes to send, and then sends her qubit to Bob in (3) which he can use in combination with the entangled qubit he started with to extract the two bits of information Alice wanted to send him.

Now for this protocol to work, as you noticed, Alice has to be able to send a qubit, or more generally some sort of quantum state, to Bob. Generally, the best way to do so is to send the desired quantum state with photons in some appropriate basis (like photon number, photon polarization, early/late time binning, etc.), but implementing this process practically is an active area of research in the field of quantum communications, specifically quantum networking.

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  • $\begingroup$ When I read it, it seemed that first an entangled pair was generated and the qubits were already distributed, one stayed with Alice and the other with Bob. And then Alice would send her qubit to Bob. Now I think I understand: Alice receives the pair |00⟩, does the entanglement, encodes and then sends the pair to Bob to decode. Both Alice and Bob act in the two qubis, Alice first, Bob second. The way Alice transfers the pair to Bob is through an appropriate medium. If I'm wrong, please tell me and thank you very much Chris. $\endgroup$
    – Student
    Commented May 18, 2023 at 1:27
  • $\begingroup$ @Student This would be pointless. A would rather send the classical information to B instead. $\endgroup$ Commented Jul 21, 2023 at 18:29

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